空间证明的复杂性理论方法
A Complexity-Theoretic Approach to Proofs of Space
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中文总结 AI 辅助
该研究提出从去随机化假设与密码学假设结合构造空间证明（PoS）的基础框架，给出实例，证明非平凡及近最优PoS可由相关假设得出，推进了PoS在非随机预言模型下的安全构造。
中文摘要 AI 辅助
空间证明（Proof of Space, PoS）是由Dziembowski等人[CRYPTO'15]提出的两阶段协议，能让证明者向高效验证者证明其已分配大量持久内存用于存储某些信息。据我们所知，所有现有PoS协议仅在随机预言模型下（或基于临时密码学假设）被证明安全。我们提供了一个从去随机化假设和密码学假设结合构造PoS的基础框架，并给出该框架的几个简单实例。我们证明非平凡PoS可由以下条件得出：(a) E=DTIME[2^{O(n)}]对指数规模非确定性电路困难（该假设用于证明AM=NP），以及(b) 抗碰撞哈希函数。我们还证明具有近最优参数和交互模式的PoS可由上述假设(a)和(c) 针对P的SNARGs得出。
英文摘要
A Proof of Space, PoS, as introduced by Dziembowski et al. [CRYPTO'15], is a two-phase protocol that enables a Prover to convince an efficient Verifier that it has allocated a large amount of persistent memory to storing some information. To our knowledge, all existing PoS protocols are only known to be secure in the random oracle model (or under ad hoc assumptions about cryptographic assumptions). We provide an elementary framework for constructing PoS from a combination of derandomization assumptions and cryptographic assumptions. We provide a few simple instantiations of the framework. We show that non-trivial PoS follow from (a) $\mathsf{E}=\mathsf{DTIME[2^{O(n)}]}$ is hard for exponential-size nondeterministic circuits (an assumption introduced to show $\mathsf{AM}=\mathsf{NP}$), and (b) collision-resistant hash functions. We also show that PoS with nearly optimal parameters and interaction pattern follows from assumption (a) above and (c) SNARGs for $\mathsf{P}$.
